Subtract $ \dfrac{2x-1}{2} $ from $ \dfrac{2x+3}{4} $ to get $ \dfrac{ \color{purple}{ -2x+5 } }{ 4 }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{2}$.

$$ \begin{aligned} \frac{2x+3}{4} - \frac{2x-1}{2} & = \frac{ 2x+3 }{ 4 } - \frac{ \left( 2x-1 \right) \cdot \color{blue}{ 2 }}{ 2 \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ 2x+3 } }{ 4 } - \frac{ \color{purple}{ 4x-2 } }{ 4 }=\frac{ \color{purple}{ 2x+3 - \left( 4x-2 \right) } }{ 4 } = \\[1ex] &=\frac{ \color{purple}{ -2x+5 } }{ 4 } \end{aligned} $$